A235999 - OEIS

%I #39 Aug 06 2015 17:30:52

%S 2,4,4,8,6,20,4,56,8,88,48,4,176,144,8,272,448,6,428,1168,8,688,2496,

%T 384,4,1044,5416,1344,12,1584,10864,4608,4,2424,21328,13152,8,3800,

%U 40096,35616,8,5656,76336,84864,3840,10,8952,140248,200224,15360

%N Triangle read by rows: T(n,k) = 2^k*A235998(n,k), n>=1, k>=1.

%C T(n,k) is also the number of overcompositions of n having k distinct parts. For the definition of overcomposition see A236002.

%C Row n has length A003056(n) hence the first element of column k is in row A000217(k).

%C Row sums give A236002, n >= 1.

%C Column 1 is A062011.

%C T(k*(k+1)/2,k) = T(A000217(k),k) = A000165(k) = (2*k)!!. - _Alois P. Heinz_, Jan 20 2014

%H Alois P. Heinz, <a href="/A235999/b235999.txt">Rows n = 1..500, flattened</a>

%e Triangle begins:

%e 2;

%e 4;

%e 4,     8;

%e 6,    20;

%e 4,    56;

%e 8,    88,     48;

%e 4,   176,    144;

%e 8,   272,    448;

%e 6,   428,   1168;

%e 8,   688,   2496,    384;

%e 4,  1044,   5416,   1344;

%e 12, 1584,  10864,   4608;

%e 4,  2424,  21328,  13152;

%e 8,  3800,  40096,  35616;

%e 8,  5656,  76336,  84864,  3840;

%e 10, 8952, 140248, 200224, 15360;

%e ...

%Y Cf. A003056, A011782, A062011, A116608, A235790, A235998, A236002.

%K nonn,tabf,look

%O 1,1

%A _Omar E. Pol_, Jan 19 2014

%E More terms from _Alois P. Heinz_, Jan 20 2014